/***********************************************************************/
/*                                                                     */
/*   svm_loqo.c                                                        */
/*                                                                     */
/*   Interface to the PR_LOQO optimization package for SVM.            */
/*                                                                     */
/*   Author: Thorsten Joachims                                         */
/*   Date: 19.07.99                                                    */
/*                                                                     */
/*   Copyright (c) 1999  Universitaet Dortmund - All rights reserved   */
/*                                                                     */
/*   This software is available for non-commercial use only. It must   */
/*   not be modified and distributed without prior permission of the   */
/*   author. The author is not responsible for implications from the   */
/*   use of this software.                                             */
/*                                                                     */
/***********************************************************************/

# include <math.h>
# include "pr_loqo/pr_loqo.h"
# include "svm_common.h"

/* Common Block Declarations */

long verbosity;

/* /////////////////////////////////////////////////////////////// */

# define DEF_PRECISION_LINEAR    1E-8
# define DEF_PRECISION_NONLINEAR 1E-14

double *optimize_qp();
double *primal=0,*dual=0;
double init_margin=0.15;
long   init_iter=500,precision_violations=0;
double model_b;
double opt_precision=DEF_PRECISION_LINEAR;

/* /////////////////////////////////////////////////////////////// */

void *my_malloc();

double *optimize_qp(qp,epsilon_crit,nx,threshold,learn_parm)
QP *qp;
double *epsilon_crit;
long nx; /* Maximum number of variables in QP */
double *threshold;
LEARN_PARM *learn_parm;
/* start the optimizer and return the optimal values */
{
    register long i,j,result;
    double margin,obj_before,obj_after;
    double sigdig,dist,epsilon_loqo;
    int iter;

    if(!primal) { /* allocate memory at first call */
        primal=(double *)my_malloc(sizeof(double)*nx*3);
        dual=(double *)my_malloc(sizeof(double)*(nx*2+1));
    }

    if(verbosity>=4) { /* really verbose */
        printf("\n\n");
        for(i=0; i<qp->opt_n; i++) {
            printf("%f: ",qp->opt_g0[i]);
            for(j=0; j<qp->opt_n; j++) {
                printf("%f ",qp->opt_g[i*qp->opt_n+j]);
            }
            printf(": a%ld=%.10f < %f",i,qp->opt_xinit[i],qp->opt_up[i]);
            printf(": y=%f\n",qp->opt_ce[i]);
        }
        for(j=0; j<qp->opt_m; j++) {
            printf("EQ-%ld: %f*a0",j,qp->opt_ce[j]);
            for(i=1; i<qp->opt_n; i++) {
                printf(" + %f*a%ld",qp->opt_ce[i],i);
            }
            printf(" = %f\n\n",-qp->opt_ce0[0]);
        }
    }

    obj_before=0; /* calculate objective before optimization */
    for(i=0; i<qp->opt_n; i++) {
        obj_before+=(qp->opt_g0[i]*qp->opt_xinit[i]);
        obj_before+=(0.5*qp->opt_xinit[i]*qp->opt_xinit[i]*qp->opt_g[i*qp->opt_n+i]);
        for(j=0; j<i; j++) {
            obj_before+=(qp->opt_xinit[j]*qp->opt_xinit[i]*qp->opt_g[j*qp->opt_n+i]);
        }
    }

    result=STILL_RUNNING;
    qp->opt_ce0[0]*=(-1.0);
    /* Run pr_loqo. If a run fails, try again with parameters which lead */
    /* to a slower, but more robust setting. */
    for(margin=init_margin,iter=init_iter;
            (margin<=0.9999999) && (result!=OPTIMAL_SOLUTION);) {
        sigdig=-log10(opt_precision);

        result=pr_loqo((int)qp->opt_n,(int)qp->opt_m,
                       (double *)qp->opt_g0,(double *)qp->opt_g,
                       (double *)qp->opt_ce,(double *)qp->opt_ce0,
                       (double *)qp->opt_low,(double *)qp->opt_up,
                       (double *)primal,(double *)dual,
                       (int)(verbosity-2),
                       (double)sigdig,(int)iter,
                       (double)margin,(double)(qp->opt_up[0])/4.0,(int)0);

        if(isnan(dual[0])) {     /* check for choldc problem */
            if(verbosity>=2) {
                printf("NOTICE: Restarting PR_LOQO with more conservative parameters.\n");
            }
            if(init_margin<0.80) { /* become more conservative in general */
                init_margin=(4.0*margin+1.0)/5.0;
            }
            margin=(margin+1.0)/2.0;
            (opt_precision)*=10.0;   /* reduce precision */
            if(verbosity>=2) {
                printf("NOTICE: Reducing precision of PR_LOQO.\n");
            }
        } else if(result!=OPTIMAL_SOLUTION) {
            iter+=2000;
            init_iter+=10;
            (opt_precision)*=10.0;   /* reduce precision */
            if(verbosity>=2) {
                printf("NOTICE: Reducing precision of PR_LOQO due to (%ld).\n",result);
            }
        }
    }

    if(qp->opt_m)         /* Thanks to Alex Smola for this hint */
        model_b=dual[0];
    else
        model_b=0;

    /* Check the precision of the alphas. If results of current optimization */
    /* violate KT-Conditions, relax the epsilon on the bounds on alphas. */
    epsilon_loqo=1E-10;
    for(i=0; i<qp->opt_n; i++) {
        dist=-model_b*qp->opt_ce[i];
        dist+=(qp->opt_g0[i]+1.0);
        for(j=0; j<i; j++) {
            dist+=(primal[j]*qp->opt_g[j*qp->opt_n+i]);
        }
        for(j=i; j<qp->opt_n; j++) {
            dist+=(primal[j]*qp->opt_g[i*qp->opt_n+j]);
        }
        /*  printf("LOQO: a[%d]=%f, dist=%f, b=%f\n",i,primal[i],dist,dual[0]); */
        if((primal[i]<(qp->opt_up[i]-epsilon_loqo)) && (dist < (1.0-(*epsilon_crit)))) {
            epsilon_loqo=(qp->opt_up[i]-primal[i])*2.0;
        } else if((primal[i]>(0+epsilon_loqo)) && (dist > (1.0+(*epsilon_crit)))) {
            epsilon_loqo=primal[i]*2.0;
        }
    }

    for(i=0; i<qp->opt_n; i++) { /* clip alphas to bounds */
        if(primal[i]<=(0+epsilon_loqo)) {
            primal[i]=0;
        } else if(primal[i]>=(qp->opt_up[i]-epsilon_loqo)) {
            primal[i]=qp->opt_up[i];
        }
    }

    obj_after=0;  /* calculate objective after optimization */
    for(i=0; i<qp->opt_n; i++) {
        obj_after+=(qp->opt_g0[i]*primal[i]);
        obj_after+=(0.5*primal[i]*primal[i]*qp->opt_g[i*qp->opt_n+i]);
        for(j=0; j<i; j++) {
            obj_after+=(primal[j]*primal[i]*qp->opt_g[j*qp->opt_n+i]);
        }
    }

    /* if optimizer returned NAN values, reset and retry with smaller */
    /* working set. */
    if(isnan(obj_after) || isnan(model_b)) {
        for(i=0; i<qp->opt_n; i++) {
            primal[i]=qp->opt_xinit[i];
        }
        model_b=0;
        if(learn_parm->svm_maxqpsize>2) {
            learn_parm->svm_maxqpsize--;  /* decrease size of qp-subproblems */
        }
    }

    if(obj_after >= obj_before) { /* check whether there was progress */
        (opt_precision)/=100.0;
        precision_violations++;
        if(verbosity>=2) {
            printf("NOTICE: Increasing Precision of PR_LOQO.\n");
        }
    }

    if(precision_violations > 500) {
        (*epsilon_crit)*=10.0;
        precision_violations=0;
        if(verbosity>=1) {
            printf("\nWARNING: Relaxing epsilon on KT-Conditions.\n");
        }
    }

    (*threshold)=model_b;

    if(result!=OPTIMAL_SOLUTION) {
        printf("\nERROR: PR_LOQO did not converge. \n");
        return(qp->opt_xinit);
    } else {
        return(primal);
    }
}

